hi everyone mehmet is here today i will
talk about creating 3d math art on
geogebra
and here is the house i just created
guys on a 3d calculator
everything you see here was created on
r3
the real coordinate space by only using
points and polygons
by only using mathematics it is cool
right
let's get started
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okay i started recording math art videos
couple of months ago and i recorded four
desmos art videos but desmos is not the
only place you can do art
in mathematics there are a few more
platforms and one of them
is geogebra geogebra is different
because you can work on
real coordinate space on r3 you can
create
3d math art on geogebra let me introduce
geogebra to you first and then
we will work on the real coordinate
space
here is the website geogebra.org 3d
the audio pro is a lot of stuff and this
is the link for
3d calculator you can find a link in the
description below
first of all don't forget to log in the
website you can use your google account
or some other accounts here to do that
okay
be logged in i don't know why but my
profile picture
doesn't show up here when you open the
link you will see this screen
on the right 3d space and on the left
the input
column let me talk about the space first
you need to know the x y plane and the
axis
the gray area you see represent the x y
plane
so red and green are x and y axes
and z is perpendicular to both the blue
one
to remember this easily you can use the
abbreviation rgb
you know rgb means the lighting system
it is very popular in gaming
it basically means red green and blue
rgb the first letters
the order of letters matched with xyz
basically rgb equals xyz in order
so x is red r y is green
g and z is blue b next
you can click the settings icon on the
right top corner
and make some changes for example you
can hide the x y plane
you can also use your mouse and rotate
the space just like that
for example if you look at from the top
it will look like the classic coordinate
plane
x y plane right okay let's start with a
point
you can write points on the space a
capital letter
equal sign open the brackets write x y z
coordinates and close it
here's the point and it is 3d so we can
see it from all different angles
let's write another point great
there is also tools option here when you
click more you will
see a lot of them this is awesome you
can use
all these tools in this video i will
focus on
two of them point tool and polygon tool
these are enough to start
3d math art first of all i am going to
start with the base of the project we
usually choose the xy plane as the base
that's why i am going to rotate the
space and make it look like the classic
coordinate plane
i am doing this because it is easier to
work on the coordinate plane
for the base now i'm going to add the
points you can of course
tie points manually but this tool the
point
tool is great and it is super easy to
use it's a must if you want to choose
points on the xy plane
let's choose some points here i am going
to choose the origin first
and if you get closer to integer values
it automatically goes to that value
the scope closer to the intersection of
integer values
and it goes to the point great now the
points are ready
for corners i'm going to create a
rectangular base here
let's choose the polygon tool and create
the base start with one one of the
points
and then choose other points in order
and finally
choose the point you started so here's
my abcd polygon
here's how it looks like on the space
okay let's go back to
2d weave and then create the base of the
house let me choose four points here
okay i think it's good let's connect
them now great
now the base is ready we can work on the
z-axis
one thing you need to know guys z-axis
basically means the height
because we are using x-y-plane as the
base so if you need a point higher than
the base
you need to add positive z values lower
than the base
means negative z values i'm going to add
some points here
um you don't have to name them because
if we just write the coordinates it
automatically names it at a good
so the point i will add will be higher
than the point e
um e coordinates are 2 4 and 0. if i add
z values it gives me some points higher
these one here you see if i increase z
values the points will be higher and
higher
so i will make it four okay here it is
2 4 4. now i'm going to check f g
h and add 4 z units there too
because i'm going to create the ceiling
after that i will turn
this shape into rectangular prism there
are of course different ways to create
rectangular prisms guys
and this is the basic one now my 8
points are ready
it is time to combine them by using the
polygon tool
connect the points four by four um you
will get a rectangular prism
now let's work on the roof i'm gonna do
a pyramid roof guys
so i need an apex point at the top x
will be four
and y will be 3 right it will be at the
center if you do that
so we also need the height 5 is good
yes then i'm going to use the polygon
tool and create the faces
let's color the roof let's make it red
choose the face you want to color
when you choose a face it will be shaded
just like that
and then click this icon color icon
click plus
to get more choose the color you want
and change the opacity
i want to set it to 100 percent
let's color other faces as well
great now i'm going to color down the
walls of the building
maybe something like gray will be good i
don't know
yes let's keep it like that you don't
have to close the the coloring menu by
the way you can just continue
choosing and moving the graph okay now
you see all the points are visible you
can hide them
but the input column is too complicated
finding points will
will take a lot of time so i'm gonna
change the settings
um click the settings icon then go to
settings
go to graph icon on the right and then
change
this one to order them by type now the
input
list changed everything is ordered group
by group it's really useful
let's check this out okay all the points
are at the top right now
that's great we can hide them all right
now
wonderful
let's change the color for the ground
okay
it is time to create a door and a few
windows for the for the door
i will choose two points at the base of
the house um
x is 3.5 for one side and
and 4.5 for the other side is good
now i need two points on top of them
copy these points guys and then add the
z
value zz1 is good
okay this is good for the door i can
choose the polygon now
the thing is after i color the door guys
it will look like that because
dark gray is at the bottom and another
color at the top
it creates like a glowing effect so we
need to get rid of this gray color
one solution is we can change the
polygon the polygon that faces us
the front face of the house is created
by the points
f j k and g i will change this
let's unhide the points first if you
don't know what
points to unhide you can unhide all of
them since all the points are at the top
i'll look at this now here's the polygon
now i'm adding other corners and make it
around the door
great no gloving effect anymore let's
add the windows
we just need to choose the points on the
space again
x is 2.5 and y is 2 on the face
and you need to play around with the z
values and get the points
okay these points look good now um let's
let's create the polygon
if you think the window is bigger than
you want um you can double click
and change the values you can make
things smaller
or bigger if you need
let's color the windows
um the same effect appeared here as well
but
you know what it looks perfect for
windows right i will keep it like that
it looks like a normal window i always
like this effect on windows
i was planning to do a two-story
building but i changed my mind
i'm gonna make it smaller let's change
the points and make the house shorter
double click the point and then change
the z value remember guys
z means height
yeah it looks good now let's hide all
the points and the segments
it is time to add a chimney i am going
to add the base here
in order to do that lets change the
opacity of the roof don't make it
zero because it will be really hard to
change it from zero
let me add a point on the ceiling and
it's gonna be the base of the chimney
let's see first thing first create the
bases
um okay it's good now i will copy paste
change the values and create the base
it may not be really visible from the
angle you are working on so you can
always change the angle
you can also color everything at the end
so if you do that you don't have to
deal with these problems by the way for
all the projects create the base first
then change z values and then create the
object now you see the points are ready
let's connect them and color them
i'm going to make the ground darker
i will also create a doorstep here
one more step will be good first the
base then the top
connect the point with the polygon tool
and then color
finally let's create the walls of the
garden
base first then the top part connect the
points and then color them
okay our first 3d geogebra project is
ready we worked on the coordinate space
r3 and i used guys points and polygons
to create this beautiful
3d object it is wonderful right and if
you want to send this to your friends
your teachers your students
click this menu icon first save the
graph and then click the share icon it
gives you the link to share
there are also several options and one
very cool thing is you can
download this as a 3d object and then
3d print it i will just change the
thickness
and let's download it great look at this
guys here's the object
my project in 3d print app it also tells
you
how much probably it costs if you print
it wonderful right
it would be great to keep your first
ever 3d math art on your desk
you can also open this with 3d viewer
and work on
these cool effects of course there are
different software to create 3d objects
but we are creating 3d objects by only
and only using mathematics
it is cool right
this is the one and only 3d geogebra
math art video on youtube
and i hope i hope you liked the video
guys i hope you liked the
3d house we just created on geogebra and
if you do
don't forget to like the video and
subscribe to my youtube channel for more
tutorials
this is the first video we just focused
on points and polygons here
but um i'm going to create guys more
tutorials soon
and after you try this i believe you
will like working with
messing around with 3d objects on the
coordinate space
learning how things work in 3d is super
cool
and i definitely recommend all of you to
try this out okay
that's it for today if you have any
questions just comment below and let me
know
i'll be with you another video about
online teaching keep watching
mathematics
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goodbye
you